Link to shiny app: https://michaeldgarber.shinyapps.io/wf-emm/
Do and colleagues have recently estimated spatially varying effects of short-term exposure to wildfire PM2.5 on acute-care hospitalizations (Do et al. 2024) in California. They defined the exposure as a day with wildfire smoke PM2.5 ≥15 μg/m3. The outcome was the number of respiratory emergency department visits and unplanned hospitalizations.
They used a case-crossover design to estimate effects at the level of the zip-code tabulation area (ZCTA) throughout 1,396 ZCTAs in California. A map of these spatially varying effect estimates, expressed as a rate difference per 100,000 person-days, appears below (adapted from their figure 5).
A positive rate difference (shades of green) indicates that wildfire had an estimated harmful effect (i.e., more) hospitalizations, while a negative value (purple shades) implies that wildfire led to fewer hospitalizations.
In addition, they explored community characteristics possibly driving this spatial heterogeneity. The authors state:
We used meta‐regression to evaluate potential effect modification by community characteristics on the effect of a wildfire smoke day on acute care utilization at the ZCTA level. For each community characteristic, which was selected a priori, we ran a meta‐regression of the pooled ZCTA‐specific rate difference on the community characteristic. To preserve statistical power, we excluded 100 ZCTAs without complete data for 14 community characteristics other than A/C prevalence, and we excluded 274 ZCTAs for meta‐regression of the A/C prevalence. Our estimates are reported as rate difference per interquartile range increase of the community characteristic.
Below, adapted from their figure 6, is a plot of the increase in rate difference per interquartile range (IQR) increase for each socio-demographic community characteristic they considered:
This analysis of effect modification describes how the estimated effect of wildfire smoke on acute-care utilization varies based on variation in the community characteristics. Results show, for example, that the wildfire-utilization effect was stronger in communities with lower levels of air conditioning and with higher levels of uninsured populations.
Interpreting a specific value from the figure, an increase in A/C proportion from the 25th percentile to the 75th percentile was associated with a 0.239 (95% confidence interval: 0.0672, 0.411) lower rate rate difference in the effect of wildfire smoke on same-day respiratory acute-care utilization.
For reference, the distribution of each effect measure modifier over the ZCTAs are as follows:
The present analysis has two goals.
The first is to explore how the distribution of the wildfire-healthcare utilization effect might change were there an intervention changing the values of the effect modifiers. For example, if all zip codes had the AC prevalence of those ZCTAs in the top AC quartile, how many hospitalizations could be averted?
Such an analysis could inform how much health could be averted by intervening upon the effect modifiers.
This analysis requires a major assumption that the effect modifiers have a causal effect on the rate difference. The goal of the analysis by Do and colleagues was not to assess causal interaction but rather effect modification, also called effect heterogeneity. The distinction between these two terms has important implications for their interpetation.
Tyler VanderWeele describes this important distinction on p. 268 of his book, Explanation in Causal Inference (bold added for emphasis here):
If we found that the effect of our primary exposure varied by strata defined by the secondary factor in this way, then we might call this “effect heterogeneity” or “effect modification.” This might be useful, for example, in decisions about which subpopulations to target in order to maximize the effect of interventions. Provided that we have controlled for confounding of relationship between the primary exposure and the outcome, these estimates of effect modification or effect heterogeneity could be useful even if we have not controlled for confounding of the relationship between the secondary factor and the outcome. (Tyler J. VanderWeele 2015)
What we would not know, however, is whether the effect heterogeneity were due to the secondary factor itself, or something else associated with it. If we have not controlled for confounding for the secondary factor, the secondary factor itself may simply be serving as a proxy for something that is causally relevant for the outcome (Tyler J. VanderWeele and Robins 2007).
VanderWeele continues (bold again added for its relevance here):
If we are interested principally in assessing the effect of the primary exposure within subgroups defined by a secondary factor then simply controlling for confounding for the relationship between the primary exposure and the outcome is sufficient. However, if we want to intervene on the secondary factor in order to change the effect of the primary exposure then we need to control for confounding of the relationships of both factors with the outcome. When we control for confounding for both factors we might refer to this as “causal interaction” in distinction from mere “effect heterogeneity” mentioned above (T. J. VanderWeele 2009).
That is, effect modification can be considered a description of variation in an effect of a primary exposure over values over a secondary variable, whereas assessment of interaction requires the secondary factor to be considered as a causal factor.
Without further analyses considering potential confounding of the effect of the effect modifiers on the outcome, the above goal can only be accomplished in an exploratory manner.
A secondary goal of this analysis is thus to explore the utility of R Shiny tools for presenting high-dimensional results with which a user can interact. For example, a user could choose to raise the distribution of the effect modifier to the 50th percentile and see how results might change. (Again, by imagining to intervene on the effect modifier, this assumes that it has a causal effect on the outcome.)
Assuming here that we can interpret the effect modifiers as causal, our approach was as follows.
We first found decile values (i.e., 10th pecentile, 20th percentile, …90th percentile, 100th percentile) for each effect measure modifier over the ZCTAs:
| emm_measure | percentile_10 | percentile_20 | percentile_25 | percentile_30 | percentile_40 | percentile_50 | percentile_60 | percentile_70 | percentile_75 | percentile_80 | percentile_90 | percentile_100 | IQR |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| above_poverty_prop | 0.471 | 0.558 | 0.589 | 0.611 | 0.665 | 0.721 | 0.764 | 0.805 | 0.821 | 0.839 | 0.878 | 0.960 | 0.232 |
| ac_prop | 0.077 | 0.206 | 0.264 | 0.333 | 0.500 | 0.625 | 0.727 | 0.825 | 0.864 | 0.904 | 1.000 | 1.000 | 0.600 |
| car_prop | 0.879 | 0.916 | 0.925 | 0.931 | 0.942 | 0.951 | 0.958 | 0.966 | 0.970 | 0.974 | 0.982 | 1.000 | 0.045 |
| edu_bach_prop | 0.104 | 0.154 | 0.175 | 0.194 | 0.240 | 0.298 | 0.355 | 0.433 | 0.475 | 0.526 | 0.650 | 0.871 | 0.300 |
| employed_prop | 0.597 | 0.650 | 0.666 | 0.679 | 0.707 | 0.727 | 0.745 | 0.759 | 0.766 | 0.774 | 0.796 | 0.918 | 0.100 |
| income_per_capita | 18244.500 | 22996.000 | 24660.250 | 26383.000 | 29999.000 | 33920.000 | 38681.000 | 44355.500 | 48049.250 | 52197.000 | 66697.500 | 163010.000 | 23389.000 |
| insured_prop | 0.817 | 0.855 | 0.867 | 0.878 | 0.897 | 0.912 | 0.925 | 0.938 | 0.944 | 0.951 | 0.966 | 1.000 | 0.077 |
| pop_dens_10k | 0.209 | 0.627 | 1.014 | 1.547 | 4.115 | 8.897 | 13.811 | 20.623 | 24.121 | 28.096 | 42.054 | 196.845 | 23.108 |
| tree_canopy_prop | 0.029 | 0.037 | 0.040 | 0.044 | 0.052 | 0.061 | 0.073 | 0.096 | 0.118 | 0.147 | 0.256 | 0.708 | 0.077 |
Then, for effect modifier and ZCTA, we calculated the difference between its baseline value and the value corresponding to each of 10 deciles. For example, if a zip code’s A/C prevalence is 50%, and we wanted to raise that zip code’s prevalence to that of the 80th percentile ZCTA, we subtracted 50% from the 80th percentile value to determine by how much its AC would have to rise to meet that of the target scenario.
percentile_by_emm_measure %>%
filter(emm_measure=="ac_prop") %>%
dplyr::select(emm_measure,percentile_80) %>%
mutate(emm_change=percentile_80-0.5)%>%
kable(digits=3)
| emm_measure | percentile_80 | emm_change |
|---|---|---|
| ac_prop | 0.904 | 0.404 |
We then expressed that change in terms of the number of IQRs that it represents.
The IQR of AC is 0.60 (above). In terms of IQRs, a change in AC from 0.5 to the 80th percentile would be 0.67 IQRs, so about two thirds of an IQR.
percentile_by_emm_measure %>%
filter(emm_measure=="ac_prop") %>%
dplyr::select(emm_measure,percentile_80, IQR) %>%
mutate(
emm_change=percentile_80-0.5,
emm_change_per_iqr=emm_change/IQR) %>%
kable(digits=3)
| emm_measure | percentile_80 | IQR | emm_change | emm_change_per_iqr |
|---|---|---|---|---|
| ac_prop | 0.904 | 0.6 | 0.404 | 0.674 |
We then calculated the new rate difference relating wildfire exposure with acute-care utilization under that alternative scenario, following this equation:
rd_target_pt=rd_baseline_pt+rd_per_ac_iqr_pt*ac_prop_change_per_iqr
where
rd_target_pt = the zip code’s new rate difference under the scenario
rd_per_ac_iqr_pt = the increase in the rate difference per change in IQR of AC
ac_prop_change_per_iqr = the number of IQRs changed in that zip code in that scenario
This equation raises at least two strong assumptions:
To consider uncertainty due to modeling error in rd_per_ac_iqr_pt and in rd_baseline_pt, in each of 1,000 replicatess, re-sample rd_baseline_pt and rd_per_ac_iqr_pt from a normal distribution using the reported standard deviation and 95% CI. We assume the confidence limit is the estimate +/- 1.96*SD.
Then, in each replicate, propagate this uncertainty throughout the calculations by re-calculating rd_target_pt using the re-sampled input values.
The resulting uncertainty interval is the 2.5th and 97.5th percentiles.
Finally, we calculated the difference in rate differences between the baseline and target scenarios.
A tabular summary of results over all ZCTAs follows.
Target percentile refers to the percentile of the effect modifier to which all ZCTAs with values below that percentile value would be raised under the target scenario. For example, if the target scenario corresponds to the 60th percentile of air conditioning, all ZCTAs below the 60th percentile would have their A/C raised to the 60th percentile.
The baseline rate difference refers to the rate difference attributable to wildfire under its status-quo value for the effect modifier. The target rate difference refers to the rate difference attributable to wildfire upon varying the ZCTA’s value of the effect modifier. The analyses below present the difference in rate differences (RDs) between these two scenarios.
An interactive dashboard with maps and results by scenario is here:
https://michaeldgarber.shinyapps.io/wf-emm/
| emm_measure_label | Target percentile | N, ZCTAs intervened | Population affected | RD per 100,000 person-days, baseline scenario | RD per 100,000 person-days, target scenario | Difference in RD per 100,000 person-days, target scenario |
|---|---|---|---|---|---|---|
| Prop. above poverty | 0.00 | 0 | 0 | 130.2 (25.6, 245.6) | 130.2 (25.6, 245.6) | 0.0 (0.0, 0.0) |
| Prop. above poverty | 0.05 | 65 | 1,427,949 | 130.2 (26.8, 245.3) | 129.3 (25.8, 244.5) | -0.9 (-1.3, -0.6) |
| Prop. above poverty | 0.10 | 130 | 3,386,555 | 130.2 (7.3, 249.2) | 127.6 (4.5, 246.4) | -2.6 (-3.2, -1.9) |
| Prop. above poverty | 0.15 | 195 | 5,771,134 | 130.2 (22.2, 239.9) | 125.4 (17.3, 234.9) | -4.8 (-5.8, -4.0) |
| Prop. above poverty | 0.20 | 259 | 7,853,094 | 130.2 (19.9, 253.2) | 123.8 (13.6, 245.8) | -6.4 (-8.0, -5.5) |
| Prop. above poverty | 0.25 | 324 | 9,829,829 | 130.2 (19.5, 230.8) | 121.6 (9.8, 222.4) | -8.6 (-10.1, -7.5) |
| Prop. above poverty | 0.30 | 389 | 12,112,618 | 130.2 (13.7, 250.8) | 119.7 (3.0, 239.0) | -10.5 (-12.5, -9.1) |
| Prop. above poverty | 0.35 | 454 | 14,286,393 | 130.2 (13.6, 250.7) | 117.0 (1.1, 237.3) | -13.2 (-15.2, -11.3) |
| Prop. above poverty | 0.40 | 518 | 16,496,408 | 130.2 (21.7, 250.1) | 114.0 (4.3, 234.4) | -16.2 (-18.3, -14.0) |
| Prop. above poverty | 0.45 | 583 | 18,774,848 | 130.2 (8.5, 256.7) | 110.0 (-10.9, 237.5) | -20.3 (-22.4, -17.6) |
| Prop. above poverty | 0.50 | 648 | 20,249,751 | 130.2 (13.5, 245.8) | 106.2 (-10.4, 222.6) | -24.0 (-26.3, -21.3) |
| Prop. above poverty | 0.55 | 713 | 22,233,303 | 130.2 (33.2, 275.2) | 102.6 (4.1, 247.5) | -27.6 (-30.3, -24.5) |
| Prop. above poverty | 0.60 | 777 | 24,099,326 | 130.2 (36.7, 249.4) | 99.1 (5.4, 219.0) | -31.1 (-34.1, -28.0) |
| Prop. above poverty | 0.65 | 842 | 25,819,346 | 130.2 (27.7, 266.1) | 94.8 (-7.7, 230.3) | -35.4 (-38.7, -32.6) |
| Prop. above poverty | 0.70 | 907 | 27,906,503 | 130.2 (33.8, 226.0) | 90.8 (-5.4, 189.3) | -39.4 (-43.3, -35.6) |
| Prop. above poverty | 0.75 | 972 | 29,901,613 | 130.2 (24.6, 264.4) | 87.3 (-20.9, 222.1) | -43.0 (-46.2, -39.0) |
| Prop. above poverty | 0.80 | 1,036 | 31,805,782 | 130.2 (-1.7, 219.3) | 82.9 (-48.9, 172.5) | -47.3 (-51.4, -43.3) |
| Prop. above poverty | 0.85 | 1,101 | 33,708,205 | 130.2 (7.7, 218.6) | 78.7 (-43.1, 165.4) | -51.5 (-55.1, -46.7) |
| Prop. above poverty | 0.90 | 1,166 | 35,553,444 | 130.2 (19.5, 247.6) | 72.8 (-38.1, 186.1) | -57.4 (-61.7, -52.9) |
| Prop. above poverty | 0.95 | 1,231 | 37,372,157 | 130.2 (3.2, 236.7) | 64.8 (-61.5, 171.2) | -65.4 (-70.2, -60.2) |
| Prop. above poverty | 1.00 | 1,295 | 38,778,134 | 130.2 (34.6, 243.1) | 48.5 (-48.4, 163.1) | -81.7 (-86.8, -74.5) |
| Prop. with A/C | 0.00 | 0 | 0 | 130.2 (11.1, 247.5) | 130.2 (11.1, 247.5) | 0.0 (0.0, 0.0) |
| Prop. with A/C | 0.05 | 0 | 0 | 130.2 (20.1, 222.7) | 130.2 (20.1, 222.7) | 0.0 (0.0, 0.0) |
| Prop. with A/C | 0.10 | 113 | 2,424,896 | 130.2 (-11.4, 239.7) | 127.5 (-14.3, 237.0) | -2.8 (-2.9, -2.5) |
| Prop. with A/C | 0.15 | 169 | 4,381,703 | 130.2 (34.3, 261.6) | 123.4 (27.3, 255.0) | -6.8 (-7.2, -6.5) |
| Prop. with A/C | 0.20 | 225 | 6,125,460 | 130.2 (24.7, 245.0) | 119.0 (13.2, 233.3) | -11.2 (-11.8, -10.6) |
| Prop. with A/C | 0.25 | 281 | 8,234,072 | 130.2 (4.3, 240.4) | 113.3 (-12.7, 223.7) | -17.0 (-17.7, -16.0) |
| Prop. with A/C | 0.30 | 324 | 9,893,793 | 130.2 (-13.0, 243.3) | 104.8 (-37.7, 217.8) | -25.5 (-26.8, -24.6) |
| Prop. with A/C | 0.35 | 391 | 12,050,238 | 130.2 (28.6, 241.7) | 90.9 (-10.4, 202.6) | -39.3 (-40.8, -37.6) |
| Prop. with A/C | 0.40 | 439 | 13,748,601 | 130.2 (-4.2, 251.1) | 78.8 (-55.8, 198.5) | -51.4 (-53.0, -49.6) |
| Prop. with A/C | 0.45 | 505 | 15,572,846 | 130.2 (-5.8, 236.2) | 71.1 (-64.7, 176.6) | -59.1 (-61.2, -57.0) |
| Prop. with A/C | 0.50 | 558 | 17,318,023 | 130.2 (2.0, 240.3) | 53.0 (-76.2, 162.7) | -77.2 (-80.1, -74.8) |
| Prop. with A/C | 0.55 | 590 | 18,405,515 | 130.2 (17.8, 280.4) | 43.3 (-70.7, 192.8) | -86.9 (-89.4, -84.2) |
| Prop. with A/C | 0.60 | 669 | 20,280,218 | 130.2 (21.7, 241.5) | 27.6 (-83.4, 139.4) | -102.6 (-105.4, -99.3) |
| Prop. with A/C | 0.65 | 729 | 22,521,985 | 130.2 (13.8, 247.1) | 12.0 (-103.2, 128.4) | -118.2 (-122.3, -114.3) |
| Prop. with A/C | 0.70 | 785 | 24,601,137 | 130.2 (18.3, 251.1) | -0.7 (-111.1, 120.4) | -130.9 (-135.9, -126.9) |
| Prop. with A/C | 0.75 | 840 | 26,517,443 | 130.2 (22.0, 254.7) | -13.1 (-123.6, 112.9) | -143.3 (-147.3, -139.7) |
| Prop. with A/C | 0.80 | 897 | 28,591,196 | 130.2 (-2.3, 248.7) | -27.3 (-159.3, 92.0) | -157.5 (-161.5, -153.2) |
| Prop. with A/C | 0.85 | 953 | 30,783,714 | 130.2 (34.9, 268.0) | -47.0 (-142.7, 89.5) | -177.3 (-183.5, -172.8) |
| Prop. with A/C | 0.90 | 985 | 32,168,706 | 130.2 (27.1, 237.7) | -63.4 (-166.6, 45.0) | -193.6 (-200.0, -189.1) |
| Prop. with A/C | 0.95 | 985 | 32,168,706 | 130.2 (-0.0, 251.5) | -63.4 (-193.7, 53.5) | -193.6 (-198.7, -189.7) |
| Prop. with A/C | 1.00 | 985 | 32,168,706 | 130.2 (32.9, 212.2) | -63.4 (-166.7, 19.2) | -193.6 (-198.7, -188.4) |
| Prop. with car | 0.00 | 0 | 0 | 130.2 (35.9, 256.3) | 130.2 (35.9, 256.3) | 0.0 (0.0, 0.0) |
| Prop. with car | 0.05 | 64 | 1,781,267 | 130.2 (16.9, 242.6) | 119.8 (6.9, 232.1) | -10.4 (-11.8, -8.9) |
| Prop. with car | 0.10 | 130 | 3,892,158 | 130.2 (33.0, 260.0) | 114.3 (17.4, 244.3) | -15.9 (-17.6, -14.4) |
| Prop. with car | 0.15 | 194 | 5,981,849 | 130.2 (43.8, 265.9) | 109.4 (24.1, 244.0) | -20.8 (-22.6, -19.1) |
| Prop. with car | 0.20 | 257 | 8,028,535 | 130.2 (39.5, 245.0) | 105.7 (15.2, 221.2) | -24.6 (-26.5, -22.5) |
| Prop. with car | 0.25 | 315 | 9,904,212 | 130.2 (-19.3, 274.7) | 102.4 (-47.2, 247.6) | -27.8 (-30.1, -26.0) |
| Prop. with car | 0.30 | 382 | 12,387,790 | 130.2 (-24.7, 258.4) | 99.7 (-55.5, 228.7) | -30.5 (-33.0, -28.3) |
| Prop. with car | 0.35 | 448 | 14,472,052 | 130.2 (31.8, 246.9) | 97.0 (-1.6, 212.4) | -33.2 (-35.7, -31.1) |
| Prop. with car | 0.40 | 516 | 16,574,631 | 130.2 (20.0, 246.1) | 93.3 (-16.2, 208.1) | -36.9 (-39.2, -34.7) |
| Prop. with car | 0.45 | 579 | 18,541,827 | 130.2 (31.1, 228.5) | 90.5 (-7.8, 189.7) | -39.7 (-42.1, -37.7) |
| Prop. with car | 0.50 | 643 | 20,824,532 | 130.2 (15.3, 246.8) | 86.6 (-27.9, 203.8) | -43.6 (-46.3, -41.2) |
| Prop. with car | 0.55 | 702 | 22,937,992 | 130.2 (7.7, 235.8) | 84.0 (-38.5, 191.6) | -46.2 (-49.0, -43.1) |
| Prop. with car | 0.60 | 771 | 25,442,245 | 130.2 (26.7, 228.0) | 80.2 (-22.8, 176.9) | -50.0 (-52.2, -48.0) |
| Prop. with car | 0.65 | 832 | 27,619,789 | 130.2 (19.1, 234.9) | 76.1 (-36.3, 181.2) | -54.1 (-56.6, -51.2) |
| Prop. with car | 0.70 | 903 | 29,701,003 | 130.2 (13.5, 255.2) | 71.7 (-45.8, 197.1) | -58.6 (-61.3, -55.6) |
| Prop. with car | 0.75 | 964 | 31,615,690 | 130.2 (3.3, 243.8) | 66.9 (-60.2, 179.9) | -63.3 (-66.3, -59.8) |
| Prop. with car | 0.80 | 1,031 | 33,569,596 | 130.2 (11.0, 241.1) | 61.8 (-57.7, 173.3) | -68.5 (-71.9, -65.9) |
| Prop. with car | 0.85 | 1,089 | 35,177,733 | 130.2 (8.3, 237.9) | 57.7 (-64.5, 166.0) | -72.5 (-75.2, -69.9) |
| Prop. with car | 0.90 | 1,166 | 36,792,942 | 130.2 (33.7, 247.4) | 51.2 (-45.3, 167.4) | -79.0 (-81.4, -76.1) |
| Prop. with car | 0.95 | 1,223 | 37,995,094 | 130.2 (11.9, 241.1) | 41.3 (-76.8, 150.8) | -88.9 (-92.9, -85.6) |
| Prop. with car | 1.00 | 1,274 | 38,726,393 | 130.2 (21.8, 267.7) | 22.1 (-83.0, 160.4) | -108.1 (-111.8, -104.7) |
| Prop. with bachelor’s degree | 0.00 | 0 | 0 | 130.2 (21.8, 238.8) | 130.2 (21.8, 238.8) | 0.0 (0.0, 0.0) |
| Prop. with bachelor’s degree | 0.05 | 65 | 1,588,344 | 130.2 (2.6, 223.1) | 129.9 (2.3, 222.8) | -0.3 (-0.4, -0.2) |
| Prop. with bachelor’s degree | 0.10 | 130 | 3,653,716 | 130.2 (18.1, 239.6) | 129.4 (17.3, 238.7) | -0.8 (-1.0, -0.6) |
| Prop. with bachelor’s degree | 0.15 | 195 | 5,611,539 | 130.2 (52.6, 245.0) | 128.7 (51.2, 243.3) | -1.5 (-1.8, -1.1) |
| Prop. with bachelor’s degree | 0.20 | 259 | 7,446,465 | 130.2 (-3.9, 249.5) | 127.8 (-6.3, 247.1) | -2.4 (-2.9, -2.1) |
| Prop. with bachelor’s degree | 0.25 | 324 | 9,571,063 | 130.2 (30.9, 251.4) | 126.8 (27.5, 248.3) | -3.4 (-4.0, -2.9) |
| Prop. with bachelor’s degree | 0.30 | 389 | 12,057,213 | 130.2 (13.2, 228.2) | 125.6 (9.0, 223.2) | -4.6 (-5.2, -4.0) |
| Prop. with bachelor’s degree | 0.35 | 454 | 13,877,003 | 130.2 (25.3, 242.3) | 124.1 (19.4, 235.5) | -6.1 (-6.9, -5.1) |
| Prop. with bachelor’s degree | 0.40 | 518 | 15,837,488 | 130.2 (3.5, 245.5) | 122.1 (-4.4, 237.3) | -8.1 (-9.0, -7.1) |
| Prop. with bachelor’s degree | 0.45 | 583 | 17,983,529 | 130.2 (30.5, 256.7) | 119.3 (19.7, 245.7) | -10.9 (-12.2, -9.9) |
| Prop. with bachelor’s degree | 0.50 | 648 | 19,663,177 | 130.2 (30.3, 224.6) | 116.5 (16.6, 209.9) | -13.8 (-15.0, -12.3) |
| Prop. with bachelor’s degree | 0.55 | 713 | 21,754,737 | 130.2 (27.8, 248.3) | 113.2 (11.2, 230.9) | -17.1 (-18.8, -15.2) |
| Prop. with bachelor’s degree | 0.60 | 778 | 23,818,070 | 130.2 (17.1, 232.2) | 109.6 (-3.3, 210.9) | -20.6 (-22.3, -18.4) |
| Prop. with bachelor’s degree | 0.65 | 842 | 25,779,658 | 130.2 (6.2, 235.5) | 104.3 (-19.8, 211.5) | -26.0 (-28.8, -23.4) |
| Prop. with bachelor’s degree | 0.70 | 907 | 27,670,377 | 130.2 (0.2, 244.5) | 98.6 (-31.2, 212.2) | -31.6 (-34.3, -29.1) |
| Prop. with bachelor’s degree | 0.75 | 972 | 29,840,689 | 130.2 (23.4, 266.5) | 92.0 (-13.6, 228.5) | -38.3 (-41.6, -35.0) |
| Prop. with bachelor’s degree | 0.80 | 1,036 | 31,824,716 | 130.2 (3.3, 239.0) | 83.3 (-44.8, 192.2) | -46.9 (-50.2, -43.5) |
| Prop. with bachelor’s degree | 0.85 | 1,101 | 33,756,697 | 130.2 (20.5, 242.7) | 74.0 (-35.3, 185.6) | -56.2 (-60.6, -51.1) |
| Prop. with bachelor’s degree | 0.90 | 1,166 | 35,461,026 | 130.2 (1.6, 243.7) | 60.1 (-69.1, 176.4) | -70.1 (-74.9, -64.1) |
| Prop. with bachelor’s degree | 0.95 | 1,231 | 37,233,776 | 130.2 (-10.7, 276.4) | 47.1 (-92.9, 195.3) | -83.1 (-89.8, -76.5) |
| Prop. with bachelor’s degree | 1.00 | 1,295 | 38,789,939 | 130.2 (18.4, 242.3) | 13.7 (-99.3, 130.6) | -116.5 (-123.4, -108.2) |
| Prop. employed | 0.00 | 0 | 0 | 130.2 (8.1, 236.1) | 130.2 (8.1, 236.1) | 0.0 (0.0, 0.0) |
| Prop. employed | 0.05 | 64 | 743,689 | 130.2 (20.9, 260.7) | 133.7 (23.8, 264.3) | 3.5 (2.5, 4.6) |
| Prop. employed | 0.10 | 129 | 1,772,478 | 130.2 (12.9, 246.3) | 136.8 (19.3, 252.6) | 6.6 (5.0, 7.9) |
| Prop. employed | 0.15 | 193 | 3,236,154 | 130.2 (26.9, 236.1) | 139.4 (35.8, 245.7) | 9.2 (7.7, 10.9) |
| Prop. employed | 0.20 | 257 | 4,744,824 | 130.2 (24.1, 272.8) | 142.7 (35.2, 284.4) | 12.5 (10.4, 13.9) |
| Prop. employed | 0.25 | 323 | 6,389,801 | 130.2 (11.8, 231.5) | 145.5 (26.5, 247.2) | 15.3 (13.3, 17.7) |
| Prop. employed | 0.30 | 381 | 8,110,151 | 130.2 (39.3, 255.0) | 148.2 (56.5, 272.1) | 18.0 (15.9, 20.1) |
| Prop. employed | 0.35 | 451 | 10,217,338 | 130.2 (16.0, 237.7) | 151.9 (36.7, 260.7) | 21.7 (19.4, 23.8) |
| Prop. employed | 0.40 | 518 | 12,488,709 | 130.2 (15.8, 276.4) | 155.7 (40.2, 302.5) | 25.4 (23.3, 28.3) |
| Prop. employed | 0.45 | 576 | 14,852,119 | 130.2 (22.2, 250.7) | 159.2 (50.8, 279.9) | 29.0 (25.9, 31.4) |
| Prop. employed | 0.50 | 644 | 17,127,734 | 130.2 (4.4, 264.0) | 162.5 (38.2, 297.1) | 32.3 (29.5, 35.6) |
| Prop. employed | 0.55 | 710 | 19,451,249 | 130.2 (32.8, 244.2) | 166.1 (68.8, 279.4) | 35.9 (32.5, 39.2) |
| Prop. employed | 0.60 | 775 | 21,966,825 | 130.2 (18.0, 238.6) | 170.1 (58.1, 279.4) | 39.9 (35.9, 43.0) |
| Prop. employed | 0.65 | 839 | 24,236,683 | 130.2 (9.7, 272.9) | 173.9 (52.9, 315.4) | 43.7 (40.1, 47.7) |
| Prop. employed | 0.70 | 907 | 26,767,654 | 130.2 (26.3, 279.0) | 177.3 (73.1, 325.7) | 47.0 (43.2, 50.2) |
| Prop. employed | 0.75 | 968 | 28,845,769 | 130.2 (6.0, 232.9) | 180.9 (58.3, 282.1) | 50.7 (47.4, 54.0) |
| Prop. employed | 0.80 | 1,031 | 30,895,197 | 130.2 (18.0, 248.7) | 185.6 (74.1, 303.3) | 55.4 (51.1, 58.8) |
| Prop. employed | 0.85 | 1,100 | 33,018,331 | 130.2 (-6.8, 255.5) | 192.0 (55.8, 315.7) | 61.7 (57.1, 66.3) |
| Prop. employed | 0.90 | 1,162 | 35,104,655 | 130.2 (20.4, 235.3) | 200.0 (92.6, 308.5) | 69.8 (65.6, 75.4) |
| Prop. employed | 0.95 | 1,230 | 37,223,891 | 130.2 (6.9, 239.8) | 214.9 (92.4, 326.6) | 84.7 (80.5, 89.7) |
| Prop. employed | 1.00 | 1,295 | 38,799,174 | 130.2 (1.6, 260.5) | 291.5 (162.3, 417.0) | 161.3 (153.3, 169.6) |
| Per-capita income | 0.00 | 0 | 0 | 130.2 (13.6, 235.9) | 130.2 (13.6, 235.9) | 0.0 (0.0, 0.0) |
| Per-capita income | 0.05 | 65 | 1,660,580 | 130.2 (21.3, 261.4) | 129.9 (21.1, 261.1) | -0.3 (-0.4, -0.2) |
| Per-capita income | 0.10 | 130 | 4,075,056 | 130.2 (32.3, 256.5) | 129.5 (31.7, 255.8) | -0.7 (-0.9, -0.5) |
| Per-capita income | 0.15 | 195 | 6,321,397 | 130.2 (5.7, 269.1) | 128.8 (4.3, 267.6) | -1.4 (-1.7, -1.2) |
| Per-capita income | 0.20 | 259 | 8,718,890 | 130.2 (26.3, 243.6) | 127.9 (23.7, 241.4) | -2.3 (-2.7, -2.0) |
| Per-capita income | 0.25 | 324 | 10,795,137 | 130.2 (8.2, 227.6) | 127.0 (4.9, 224.2) | -3.2 (-3.7, -2.8) |
| Per-capita income | 0.30 | 389 | 13,124,442 | 130.2 (-19.8, 281.0) | 125.9 (-23.8, 276.6) | -4.3 (-4.9, -3.8) |
| Per-capita income | 0.35 | 454 | 15,273,639 | 130.2 (24.2, 253.4) | 124.7 (18.8, 247.9) | -5.6 (-6.2, -5.0) |
| Per-capita income | 0.40 | 518 | 17,018,842 | 130.2 (15.2, 231.3) | 122.9 (7.7, 224.3) | -7.3 (-8.0, -6.4) |
| Per-capita income | 0.45 | 583 | 18,929,460 | 130.2 (7.6, 235.7) | 121.0 (-1.5, 226.8) | -9.2 (-10.2, -8.2) |
| Per-capita income | 0.50 | 648 | 20,878,760 | 130.2 (8.5, 246.5) | 118.7 (-2.1, 234.4) | -11.5 (-12.7, -10.3) |
| Per-capita income | 0.55 | 713 | 22,698,513 | 130.2 (39.7, 249.9) | 116.0 (25.4, 234.7) | -14.2 (-15.4, -13.0) |
| Per-capita income | 0.60 | 778 | 24,541,894 | 130.2 (3.4, 239.0) | 112.6 (-14.3, 220.5) | -17.6 (-19.3, -16.5) |
| Per-capita income | 0.65 | 842 | 26,519,982 | 130.2 (1.1, 232.9) | 108.9 (-18.8, 211.6) | -21.3 (-23.0, -19.3) |
| Per-capita income | 0.70 | 907 | 28,390,553 | 130.2 (31.4, 279.6) | 103.9 (6.4, 252.8) | -26.3 (-28.3, -24.2) |
| Per-capita income | 0.75 | 972 | 30,282,012 | 130.2 (22.2, 228.6) | 97.6 (-11.1, 195.6) | -32.6 (-35.2, -30.2) |
| Per-capita income | 0.80 | 1,036 | 32,233,623 | 130.2 (-7.3, 240.0) | 90.0 (-46.6, 199.6) | -40.2 (-43.2, -37.5) |
| Per-capita income | 0.85 | 1,101 | 34,003,885 | 130.2 (17.7, 231.7) | 78.9 (-31.7, 182.9) | -51.3 (-55.0, -47.8) |
| Per-capita income | 0.90 | 1,166 | 35,861,585 | 130.2 (24.2, 242.2) | 60.8 (-44.7, 169.4) | -69.4 (-74.1, -65.3) |
| Per-capita income | 0.95 | 1,231 | 37,517,547 | 130.2 (-5.2, 262.0) | 25.1 (-108.3, 156.7) | -105.1 (-111.2, -99.1) |
| Per-capita income | 1.00 | 1,295 | 38,794,645 | 130.2 (5.0, 237.9) | -160.0 (-290.7, -55.2) | -290.2 (-303.6, -272.0) |
| Proportion insured | 0.00 | 0 | 0 | 130.2 (19.1, 241.0) | 130.2 (19.1, 241.0) | 0.0 (0.0, 0.0) |
| Proportion insured | 0.05 | 65 | 2,366,874 | 130.2 (30.9, 269.8) | 126.7 (27.3, 266.3) | -3.5 (-4.2, -2.9) |
| Proportion insured | 0.10 | 130 | 4,848,130 | 130.2 (28.1, 230.2) | 122.6 (20.1, 222.4) | -7.6 (-8.6, -6.9) |
| Proportion insured | 0.15 | 195 | 6,703,232 | 130.2 (21.4, 253.8) | 117.6 (9.0, 241.6) | -12.7 (-14.1, -11.5) |
| Proportion insured | 0.20 | 259 | 8,772,506 | 130.2 (9.8, 243.3) | 112.7 (-7.2, 226.4) | -17.5 (-18.8, -15.9) |
| Proportion insured | 0.25 | 324 | 11,023,808 | 130.2 (2.9, 241.8) | 107.7 (-18.6, 219.4) | -22.5 (-24.1, -21.1) |
| Proportion insured | 0.30 | 389 | 13,343,862 | 130.2 (20.1, 232.0) | 102.2 (-6.7, 203.8) | -28.0 (-30.1, -26.1) |
| Proportion insured | 0.35 | 454 | 15,549,465 | 130.2 (26.6, 248.4) | 95.3 (-6.9, 213.1) | -34.9 (-37.2, -33.2) |
| Proportion insured | 0.40 | 518 | 17,140,063 | 130.2 (35.0, 245.2) | 90.0 (-5.6, 204.8) | -40.2 (-42.6, -38.0) |
| Proportion insured | 0.45 | 583 | 19,080,599 | 130.2 (-0.7, 221.3) | 84.9 (-44.2, 174.8) | -45.4 (-47.6, -43.1) |
| Proportion insured | 0.50 | 648 | 21,056,969 | 130.2 (29.8, 245.1) | 77.5 (-22.5, 193.2) | -52.7 (-55.3, -50.2) |
| Proportion insured | 0.55 | 713 | 23,146,449 | 130.2 (19.2, 233.5) | 70.7 (-40.6, 174.5) | -59.5 (-62.2, -56.7) |
| Proportion insured | 0.60 | 777 | 24,688,211 | 130.2 (31.6, 231.1) | 63.9 (-36.1, 165.5) | -66.3 (-69.1, -63.2) |
| Proportion insured | 0.65 | 842 | 26,679,437 | 130.2 (14.6, 234.9) | 58.9 (-57.6, 162.5) | -71.4 (-74.7, -68.5) |
| Proportion insured | 0.70 | 907 | 28,429,661 | 130.2 (12.4, 244.2) | 48.8 (-68.1, 163.7) | -81.4 (-85.1, -77.5) |
| Proportion insured | 0.75 | 972 | 30,369,580 | 130.2 (16.5, 232.5) | 40.4 (-74.8, 143.3) | -89.8 (-93.1, -86.4) |
| Proportion insured | 0.80 | 1,036 | 32,312,570 | 130.2 (4.2, 222.8) | 30.6 (-96.2, 123.0) | -99.6 (-103.9, -96.3) |
| Proportion insured | 0.85 | 1,101 | 34,174,766 | 130.2 (25.4, 251.9) | 20.6 (-84.2, 142.3) | -109.6 (-112.8, -105.2) |
| Proportion insured | 0.90 | 1,166 | 36,017,246 | 130.2 (31.2, 240.6) | 6.7 (-92.5, 117.2) | -123.5 (-127.5, -120.0) |
| Proportion insured | 0.95 | 1,231 | 37,680,657 | 130.2 (1.4, 245.6) | -8.6 (-138.3, 107.2) | -138.8 (-142.5, -133.9) |
| Proportion insured | 1.00 | 1,293 | 38,795,310 | 130.2 (17.0, 231.2) | -54.1 (-166.9, 50.6) | -184.3 (-189.2, -179.5) |
| Population density | 0.00 | 0 | 0 | 130.2 (4.5, 249.0) | 130.2 (4.5, 249.0) | 0.0 (0.0, 0.0) |
| Population density | 0.05 | 65 | 212,201 | 130.2 (54.5, 244.7) | 130.2 (54.6, 244.7) | 0.0 (0.0, 0.0) |
| Population density | 0.10 | 130 | 585,344 | 130.2 (0.5, 237.1) | 130.3 (0.5, 237.2) | 0.0 (0.0, 0.0) |
| Population density | 0.15 | 195 | 1,139,831 | 130.2 (31.9, 231.9) | 130.3 (32.0, 232.0) | 0.1 (0.1, 0.1) |
| Population density | 0.20 | 259 | 2,197,325 | 130.2 (43.3, 251.9) | 130.5 (43.6, 252.2) | 0.3 (0.3, 0.3) |
| Population density | 0.25 | 324 | 3,731,511 | 130.2 (14.9, 242.8) | 130.8 (15.5, 243.4) | 0.6 (0.6, 0.6) |
| Population density | 0.30 | 389 | 5,423,463 | 130.2 (-14.5, 230.3) | 131.3 (-13.4, 231.4) | 1.1 (1.1, 1.2) |
| Population density | 0.35 | 454 | 7,286,524 | 130.2 (38.4, 248.2) | 132.6 (40.9, 250.7) | 2.4 (2.3, 2.6) |
| Population density | 0.40 | 518 | 9,252,703 | 130.2 (31.1, 244.4) | 134.7 (35.6, 248.9) | 4.5 (4.3, 4.7) |
| Population density | 0.45 | 583 | 11,136,502 | 130.2 (24.0, 243.2) | 137.8 (31.6, 250.7) | 7.6 (7.2, 8.0) |
| Population density | 0.50 | 648 | 13,543,389 | 130.2 (26.2, 252.3) | 142.6 (38.4, 264.6) | 12.3 (11.7, 12.8) |
| Population density | 0.55 | 713 | 16,130,870 | 130.2 (-7.9, 260.1) | 147.1 (9.1, 276.6) | 16.9 (16.2, 17.5) |
| Population density | 0.60 | 778 | 18,255,568 | 130.2 (19.2, 232.7) | 152.4 (41.4, 255.5) | 22.2 (21.3, 23.2) |
| Population density | 0.65 | 842 | 20,640,265 | 130.2 (20.7, 255.5) | 159.5 (50.4, 283.9) | 29.3 (27.9, 30.7) |
| Population density | 0.70 | 907 | 22,937,642 | 130.2 (-13.5, 238.5) | 168.5 (25.1, 276.6) | 38.3 (36.7, 40.0) |
| Population density | 0.75 | 972 | 25,559,995 | 130.2 (-0.1, 260.5) | 177.7 (47.9, 308.0) | 47.5 (45.7, 49.3) |
| Population density | 0.80 | 1,036 | 28,075,902 | 130.2 (19.6, 245.7) | 188.9 (77.8, 303.9) | 58.7 (55.9, 60.4) |
| Population density | 0.85 | 1,101 | 30,450,650 | 130.2 (5.6, 249.1) | 205.1 (82.0, 326.1) | 74.9 (71.9, 78.3) |
| Population density | 0.90 | 1,166 | 33,066,517 | 130.2 (30.6, 247.9) | 232.4 (130.7, 350.3) | 102.1 (98.7, 105.8) |
| Population density | 0.95 | 1,231 | 35,800,636 | 130.2 (-6.1, 240.8) | 284.3 (144.8, 390.6) | 154.1 (148.2, 159.1) |
| Population density | 1.00 | 1,295 | 38,788,303 | 130.2 (6.0, 238.6) | 786.3 (667.6, 899.9) | 656.1 (636.7, 677.2) |
| Tree canopy share | 0.00 | 0 | 0 | 130.2 (15.7, 257.0) | 130.2 (15.7, 257.0) | 0.0 (0.0, 0.0) |
| Tree canopy share | 0.05 | 65 | 1,228,408 | 130.2 (18.3, 265.8) | 129.7 (17.8, 265.2) | -0.5 (-0.6, -0.5) |
| Tree canopy share | 0.10 | 130 | 3,598,934 | 130.2 (51.7, 237.8) | 128.5 (50.0, 236.1) | -1.7 (-1.8, -1.6) |
| Tree canopy share | 0.15 | 195 | 6,547,961 | 130.2 (22.5, 255.2) | 127.6 (19.8, 252.5) | -2.6 (-2.7, -2.5) |
| Tree canopy share | 0.20 | 259 | 9,189,388 | 130.2 (28.0, 237.0) | 126.6 (24.6, 233.3) | -3.6 (-3.8, -3.4) |
| Tree canopy share | 0.25 | 324 | 11,592,375 | 130.2 (31.6, 248.4) | 125.5 (27.0, 243.7) | -4.7 (-4.9, -4.4) |
| Tree canopy share | 0.30 | 389 | 14,175,321 | 130.2 (7.3, 247.1) | 123.8 (0.8, 240.7) | -6.4 (-6.6, -6.1) |
| Tree canopy share | 0.35 | 454 | 16,841,575 | 130.2 (8.6, 268.8) | 122.1 (0.5, 260.8) | -8.1 (-8.4, -7.8) |
| Tree canopy share | 0.40 | 518 | 19,067,769 | 130.2 (5.9, 235.7) | 119.4 (-4.8, 224.9) | -10.8 (-11.2, -10.4) |
| Tree canopy share | 0.45 | 583 | 21,319,444 | 130.2 (8.9, 249.7) | 116.8 (-4.7, 236.2) | -13.4 (-13.8, -13.0) |
| Tree canopy share | 0.50 | 648 | 23,525,351 | 130.2 (39.9, 256.9) | 113.1 (23.3, 239.9) | -17.1 (-17.6, -16.5) |
| Tree canopy share | 0.55 | 713 | 25,534,059 | 130.2 (31.7, 275.2) | 108.4 (9.7, 253.4) | -21.8 (-22.4, -21.3) |
| Tree canopy share | 0.60 | 777 | 27,497,040 | 130.2 (20.2, 250.7) | 102.7 (-7.3, 223.7) | -27.5 (-28.2, -26.6) |
| Tree canopy share | 0.65 | 842 | 29,390,968 | 130.2 (4.1, 223.4) | 93.6 (-32.5, 187.0) | -36.6 (-37.5, -35.7) |
| Tree canopy share | 0.70 | 907 | 31,378,211 | 130.2 (27.6, 245.7) | 78.9 (-22.9, 194.2) | -51.3 (-52.3, -50.0) |
| Tree canopy share | 0.75 | 972 | 33,302,304 | 130.2 (20.8, 254.3) | 54.4 (-54.5, 178.1) | -75.8 (-77.6, -73.9) |
| Tree canopy share | 0.80 | 1,036 | 35,098,620 | 130.2 (19.5, 258.8) | 19.0 (-91.9, 147.8) | -111.2 (-113.6, -108.7) |
| Tree canopy share | 0.85 | 1,101 | 36,360,331 | 130.2 (-27.2, 247.6) | -42.9 (-199.7, 73.1) | -173.1 (-176.5, -168.9) |
| Tree canopy share | 0.90 | 1,166 | 37,575,608 | 130.2 (40.1, 251.6) | -126.6 (-215.5, -4.5) | -256.8 (-260.4, -252.2) |
| Tree canopy share | 0.95 | 1,231 | 38,309,338 | 130.2 (12.5, 243.9) | -324.6 (-443.7, -211.2) | -454.8 (-463.1, -446.2) |
| Tree canopy share | 1.00 | 1,295 | 38,792,381 | 130.2 (23.8, 240.6) | -810.4 (-919.3, -696.5) | -940.6 (-955.4, -921.3) |